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Task/Numeric-error-propagation/FreeBASIC/numeric-error-propagation.basic

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+'----------------------
+' definition of a "measurement" type with value and uncartainty
+' and operators that can operate on them
+'---------------------
+
+#macro p2(x)
+    (x)*(x)
+#endmacro
+
+type meas
+    vlu as double
+    unc as double
+end type
+
+operator + ( a as meas, b as meas ) as meas
+    dim ret as meas
+    ret.vlu = a.vlu + b.vlu
+    ret.unc = sqr( a.unc*a.unc + b.unc*b.unc )
+    return ret
+end operator
+
+operator + ( c as double, a as meas ) as meas
+    dim ret as meas
+    ret.vlu = a.vlu + c
+    ret.unc = a.unc
+    return ret
+end operator
+
+operator + ( a as meas, c as double ) as meas
+    return c+a
+end operator
+
+operator - ( a as meas, b as meas ) as meas
+    dim ret as meas
+    ret.vlu = a.vlu - b.vlu
+    ret.unc = sqr( a.unc*a.unc + b.unc*b.unc )
+    return ret
+end operator
+
+operator - ( c as double, a as meas ) as meas
+    dim ret as meas
+    ret.vlu = a.vlu - c
+    ret.unc = a.unc
+    return ret
+end operator
+
+operator - ( a as meas, c as double ) as meas
+    dim ret as meas
+    ret.vlu = c - a.vlu
+    ret.unc = a.unc
+    return ret
+end operator
+
+operator * ( a as meas, b as meas ) as meas
+    dim ret as meas
+    ret.vlu = a.vlu*b.vlu
+    ret.unc = sqr(p2(ret.vlu) * (p2(a.unc/a.vlu)+p2(b.unc/b.vlu)))
+    return ret
+end operator
+
+operator * ( c as double, a as meas ) as meas
+    dim ret as meas
+    ret.vlu = a.vlu*c
+    ret.unc = abs(c*a.unc)
+    return ret
+end operator
+
+operator * ( a as meas, c as double ) as meas
+    return c*a
+end operator
+
+operator ^ ( a as meas, c as double ) as meas
+    dim ret as meas
+    ret.vlu = a.vlu ^ c
+    ret.unc = abs(ret.vlu*c*a.unc/a.vlu)
+    return ret
+end operator
+
+operator / ( c as double, a as meas ) as meas
+    return c*a^(-1)
+end operator
+
+operator / ( a as meas, c as double ) as meas
+    return a*(1.0/c)
+end operator
+
+operator / ( a as meas, b as meas ) as meas
+    return b*a^(-1)
+end operator
+
+sub printm( a as meas )
+    print using "####.##### +- ####.####"; a.vlu; a.unc
+end sub
+
+'--------------------------------
+'   now the results
+'--------------------------------
+
+dim as meas x1, y1, x2, y2
+x1.vlu = 100.
+x1.unc = 1.1
+y1.vlu = 50.
+y1.unc = 1.2
+x2.vlu = 200.
+x2.unc = 2.2
+y2.vlu = 100.
+y2.unc = 2.3
+
+printm( ((x1-x2)^2 + (y1-y2)^2)^0.5 )